I agree with the trimmer as a good place to start. This would be my list of must-haves for starting out, but of course, it all depends on what she wants to do:
-tape runner (faster and less messy)
-zig glue pen for tiny stuff
-border punch (increases the fun-factor of scrapping because you get the sense of "wow, I did that myself!"
I like OP's ideas of getting those album kits that come with a bunch of coordinated stuff. I made an album kit early in my scrapping days and it really increased my confidence and made me feel like I could make something nice (which was a shocking concept at the time). It also gives her a chance to try out a variety of supplies like chipboard pieces, brads, ribbon, letter stickers, etc.